sspt_MatrixOps Class Reference

Combine many numerical linear algebra routines. More...

#include <sspt_matrixops.h>

List of all members.

Static Public Member Functions
static bool	modifiedGramSchmidt (const sspt_Matrix &A, sspt_Matrix *Q, sspt_Matrix *R, bool full)
static bool	computeDeterminantByQR (double *result, const sspt_Matrix &A, sspt_Matrix *Q, sspt_Matrix *R)
static bool	computeInverse (sspt_Matrix *invertedMatrix, const sspt_Matrix &inputMatrix)
static void	setIdentity (sspt_Matrix *A)
static void	randomMatrix (sspt_Matrix *M)
static void	randomVector (sspt_Vector *v)
static bool	multiply (sspt_Matrix *A, const sspt_Matrix &B, const sspt_Matrix &C)
static bool	multiplyBtC (sspt_Matrix *A, const sspt_Matrix &Bt, const sspt_Matrix &C)
static bool	multiplyBCt (sspt_Matrix *A, const sspt_Matrix &B, const sspt_Matrix &Ct)
static bool	multiplyAtA (sspt_Matrix *result, const sspt_Matrix &A)
static bool	backSubstitution (const sspt_Matrix &R, sspt_Vector *x, const sspt_Vector &b)
static bool	forwardSubstitution (const sspt_Matrix &L, sspt_Vector *x, const sspt_Vector &b)
static bool	householder (const sspt_Matrix &A, sspt_Matrix *Q, sspt_Matrix *R, bool full)
static bool	householderSolve (const sspt_Matrix &A, sspt_Vector *x, const sspt_Vector &b)
static bool	givensQR (const sspt_Matrix &A, sspt_Matrix *Q, sspt_Matrix *R, bool full)
static bool	givensQRTridiagonal (const sspt_Matrix &A, sspt_Matrix *Q, sspt_Matrix *R)
static bool	PLUfactorization (const sspt_Matrix &A, sspt_Matrix *P, sspt_Matrix *L, sspt_Matrix *U)
static bool	hessenberg (const sspt_Matrix &A, sspt_Matrix *H)
static bool	cholesky (sspt_Matrix *result, const sspt_Matrix &A)
static bool	conjugateGradient (const sspt_Matrix &A, sspt_Vector *x, const sspt_Vector &b, double epsilon)
static bool	bidiagonalization (sspt_Matrix *U, sspt_Matrix *B, sspt_Matrix *V, const sspt_Matrix &A)
static bool	powerIteration (double *lambdaFinal, sspt_Vector *eigenvector, double *lambdaPerIteration, unsigned long *iterations, const sspt_Matrix &A, const sspt_Vector &initial, double epsilon, unsigned long maxIterations)
static bool	shiftedInversePowerIteration (double *lambdaFinal, sspt_Vector *eigenvector, double *lambdaPerIteration, unsigned long *iterations, const sspt_Matrix &A, const sspt_Vector &initial, double shift, double epsilon, unsigned long maxIterations)
static bool	rayleighQuotientIteration (double *lambdaFinal, sspt_Vector *eigenvector, double *lambdaPerIteration, unsigned long *iterations, const sspt_Matrix &A, const sspt_Vector &initial, double shift, double epsilon, unsigned long maxIterations)
static bool	eigenvaluesQR (sspt_Vector *eigenvalues, const sspt_Matrix &A)
static bool	conditionNumber (double *value, const sspt_Matrix &A)

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Detailed Description

Combine many numerical linear algebra routines.

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Member Function Documentation

static bool sspt_MatrixOps::backSubstitution	(	const sspt_Matrix &	R,
		sspt_Vector *	x,
		const sspt_Vector &	b
	)			[static]

static bool sspt_MatrixOps::bidiagonalization	(	sspt_Matrix *	U,
		sspt_Matrix *	B,
		sspt_Matrix *	V,
		const sspt_Matrix &	A
	)			[static]

static bool sspt_MatrixOps::cholesky	(	sspt_Matrix *	result,
		const sspt_Matrix &	A
	)			[static]

static bool sspt_MatrixOps::computeDeterminantByQR	(	double *	result,
		const sspt_Matrix &	A,
		sspt_Matrix *	Q,
		sspt_Matrix *	R
	)			[static]

static bool sspt_MatrixOps::computeInverse	(	sspt_Matrix *	invertedMatrix,
		const sspt_Matrix &	inputMatrix
	)			[static]

static bool sspt_MatrixOps::conditionNumber	(	double *	value,
		const sspt_Matrix &	A
	)			[static]

static bool sspt_MatrixOps::conjugateGradient	(	const sspt_Matrix &	A,
		sspt_Vector *	x,
		const sspt_Vector &	b,
		double	epsilon
	)			[static]

static bool sspt_MatrixOps::eigenvaluesQR	(	sspt_Vector *	eigenvalues,
		const sspt_Matrix &	A
	)			[static]

static bool sspt_MatrixOps::forwardSubstitution	(	const sspt_Matrix &	L,
		sspt_Vector *	x,
		const sspt_Vector &	b
	)			[static]

static bool sspt_MatrixOps::givensQR	(	const sspt_Matrix &	A,
		sspt_Matrix *	Q,
		sspt_Matrix *	R,
		bool	full
	)			[static]

static bool sspt_MatrixOps::givensQRTridiagonal	(	const sspt_Matrix &	A,
		sspt_Matrix *	Q,
		sspt_Matrix *	R
	)			[static]

static bool sspt_MatrixOps::hessenberg	(	const sspt_Matrix &	A,
		sspt_Matrix *	H
	)			[static]

static bool sspt_MatrixOps::householder	(	const sspt_Matrix &	A,
		sspt_Matrix *	Q,
		sspt_Matrix *	R,
		bool	full
	)			[static]

static bool sspt_MatrixOps::householderSolve	(	const sspt_Matrix &	A,
		sspt_Vector *	x,
		const sspt_Vector &	b
	)			[static]

static bool sspt_MatrixOps::modifiedGramSchmidt	(	const sspt_Matrix &	A,
		sspt_Matrix *	Q,
		sspt_Matrix *	R,
		bool	full
	)			[static]

static bool sspt_MatrixOps::multiply	(	sspt_Matrix *	A,
		const sspt_Matrix &	B,
		const sspt_Matrix &	C
	)			[static]

static bool sspt_MatrixOps::multiplyAtA	(	sspt_Matrix *	result,
		const sspt_Matrix &	A
	)			[static]

static bool sspt_MatrixOps::multiplyBCt	(	sspt_Matrix *	A,
		const sspt_Matrix &	B,
		const sspt_Matrix &	Ct
	)			[static]

static bool sspt_MatrixOps::multiplyBtC	(	sspt_Matrix *	A,
		const sspt_Matrix &	Bt,
		const sspt_Matrix &	C
	)			[static]

static bool sspt_MatrixOps::PLUfactorization	(	const sspt_Matrix &	A,
		sspt_Matrix *	P,
		sspt_Matrix *	L,
		sspt_Matrix *	U
	)			[static]

static bool sspt_MatrixOps::powerIteration	(	double *	lambdaFinal,
		sspt_Vector *	eigenvector,
		double *	lambdaPerIteration,
		unsigned long *	iterations,
		const sspt_Matrix &	A,
		const sspt_Vector &	initial,
		double	epsilon,
		unsigned long	maxIterations
	)			[static]

static void sspt_MatrixOps::randomMatrix

(

sspt_Matrix *

M

)

[static]

static void sspt_MatrixOps::randomVector

(

sspt_Vector *

v

)

[static]

static bool sspt_MatrixOps::rayleighQuotientIteration	(	double *	lambdaFinal,
		sspt_Vector *	eigenvector,
		double *	lambdaPerIteration,
		unsigned long *	iterations,
		const sspt_Matrix &	A,
		const sspt_Vector &	initial,
		double	shift,
		double	epsilon,
		unsigned long	maxIterations
	)			[static]

static void sspt_MatrixOps::setIdentity

(

sspt_Matrix *

A

)

[static]

static bool sspt_MatrixOps::shiftedInversePowerIteration	(	double *	lambdaFinal,
		sspt_Vector *	eigenvector,
		double *	lambdaPerIteration,
		unsigned long *	iterations,
		const sspt_Matrix &	A,
		const sspt_Vector &	initial,
		double	shift,
		double	epsilon,
		unsigned long	maxIterations
	)			[static]